DC Optimal Power Flow with Joint Chance Constraints

Alejandra Pena-Ordieres*, Daniel K. Molzahn, Line A. Roald, Andreas Wachter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Managing uncertainty and variability in power injections has become a major concern for power system operators due to increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a joint chance-constrained formulation of the DC optimal power flow (OPF) problem, which satisfies all the constraints jointly with a pre-determined probability. The few existing approaches for solving joint chance-constrained OPF problems are typically either computationally intractable for large-scale problems or give overly conservative solutions that satisfy the constraints far more often than required, resulting in excessively costly operation. This paper proposes an algorithm for solving joint chance-constrained DC OPF problems by adopting an S$\ell _1$QP-type trust-region algorithm. This algorithm uses a sample-based approach that avoids making strong assumptions on the distribution of the uncertainties, scales favorably to large problems, and can be tuned to obtain less conservative results. We illustrate the performance of our method using several IEEE test cases. The results demonstrate the proposed algorithm's advantages in computational times and limited conservativeness of the solutions relative to other joint chance-constrained DC OPF algorithms.

Original languageEnglish (US)
Article number9122389
Pages (from-to)147-158
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number1
StatePublished - Jan 2021


  • Joint chance constraints
  • nonlinear optimization
  • optimal power flow
  • sample average approximation

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering

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